Guoce Xin

activity

20232026

most citedA Combinatorial Approach to Frobenius Numbers of Some Special Sequences (Complete Version)

6 citations · 12 across the 23 of their papers we have counts for

collaborators

Showing 2026Show all

8 papers · 1 filter

math.CO2026

Exact Ehrhart Series of Birkhoff Polytopes via Constant Terms and Finite-Field Evaluation

Xinru Jiang, Guoce Xin, Chen Zhang +1

The Ehrhart series of the $n$ th Birkhoff polytope is $\sum_{r \geq 0} H_{n} (r) z^{r}$ , where $H_{n} (r)$ counts nonnegative integer $n \times n$ matrices whose row and column sums all equal $r…

math.CO2026

A polynomial time algorithm for almost bounded denumerant

Guoce Xin, Chen Zhang, Zihao Zhang

Sylvester's denumerant $d (t; A)$ counts the number of nonnegative integer solutions to $\sum_{i = 1}^{N} a_{i} x_{i} = t$ , where $A = (a_{1}, \dots, a_{N})$ is a se…

math.CO2026

Counterexamples to the Minimum Period Conjecture for Restricted Partition Functions

Feihu Liu, Jinlong Tang, Guoce Xin +1

For a finite sequence of positive integers $a = (a_{1}, \dots, a_{n})$ , the restricted partition function $q_{a} (k)$ denote the number of nonnegative integer solu…

math.CO2026

Root-of-unity weighted trigonometric power sums: a constant term approach

Jiahang Liu, Guoce Xin

We present a unified method for evaluating finite sums of powers of cotangent, tangent, cosecant and secant weighted by primitive $k$ th roots of unity. The approach relies on const…

math.CO2026

Ehrhart Theory of the Join of Two Lattice Polytopes

Feihu Liu, Sihao Tao, Guoce Xin

Inspired by research on the Cartesian product of two lattice polytopes, this paper investigates the Ehrhart theory of the join of two lattice polytopes. This is also a well-known o…

math.CO2026

Explicit Construction of Polytopes whose Ehrhart Polynomials Realize any Given Sign Pattern

Feihu Liu, Sihao Tao, Guoce Xin

In Ehrhart theory, the well-known sign pattern problem asks: given a positive integer $d \geq 3$ and integers $1 \leq i_{1} < \dots < i_{k} \leq d - 2$ , does there exist a $d$ -dimensiona…

math.CO2026

Unimodular Equivalence of Integral Simplices

Feihu Liu, Sihao Tao, Guoce Xin

Testing the unimodular equivalence of two full-dimensional integral simplices can be reduced to testing unimodular permutation (UP) equivalence of two nonsingular matrices. We cond…

math.CO2026

Proof of a Conjecture on Young Tableaux with Walls

Zhicong Lin, Feihu Liu, Jiahang Liu +2

Banderier, Marchal, and Wallner considered Young tableaux with walls, which are similar to standard Young tableaux, except that local decreases are allowed at some walls. In this w…